This is a site you use to test clients – mobile apps, browsers, and many other applications that use HTTP applications and TLS – the Transport Layer Security protocol. We have designed a lot of tests that checks if your browser or client application really checks the identity of the server it’s trying to connect to. It is important that developers understand how TLS works and how site verification works.

Fork us on Github

All the tests, including keys and certificates, are available on Github.
https://github.com/edvinanet/tls-o-matic
That's also where you will find all the current tests while waiting for us to write documentation here.

What is TLS?

"The TLS protocol provides communications security
over the Internet. The protocol allows client/server applications to communicate in a way that is designed to prevent eavesdropping, tampering, or message forgery."
From RFC 5446 that defines the current TLS - version 1.2. Wikipedia is also a good help in explaining TLS.